Forza Horizon 5 was launched to Steam besides Microsoft Store and Xbox, and instantly became very popular. Unfortunately, the Steam version did not support cross-saves between the others, and now we know it's the same thing with Halo Infinite.
This was confirmed by The Verge's editor Tom Warren on Twitter, who tweets:
"I started playing Halo Infinite on Steam, and I have a campaign save there. I'm now trying to play on Xbox Series X and the campaign save isn't there. Looks like this is similar to Forza Horizon 5 where cross-save only works on the Windows Store PC version. Be warned"
Probably a none-existing issue for most gamers, but still good to know if you were on of them wondering.